Ib txoj kev hloov pauv yog txhaj tshuaj yog tias tib txoj kev uas ob lub tswv yim vectors tuaj yeem tsim cov txiaj ntsig zoo ib yam yog txoj hauv kev tsis tseem ceeb, thaum ob lub tswv yim vectors sib npaug.
Kev txhaj tshuaj nyob rau hauv linear algebra yog dab tsi?
Hauv kev ua lej, ib qho kev txhaj tshuaj (tseem hu ua kev txhaj tshuaj, lossis ib-rau-ib txoj haujlwm) yog ua haujlwm f uas qhia cov ntsiab lus sib txawv rau cov ntsiab lus sib txawv ; uas yog, f(x1)=f(x2) implies x1=x 2. Hauv lwm lo lus, txhua lub ntsiab lus ntawm lub luag haujlwm lub codomain yog cov duab ntawm feem ntau ntawm nws lub npe.
Symmetric linear transformation yog dab tsi?
Nyob hauv linear algebra, ib tug symmetric matrix yog ib square matrix uas yog sib npaug rau nws transpose. Raws li txoj cai, Vim hais tias sib npaug matrices muaj qhov sib npaug sib npaug, tsuas yog square matrices tuaj yeem ua tau zoo. Cov kev nkag ntawm lub matrix symmetric yog symmetric nrog rau lub ntsiab kab pheeb ces kaum.
Puas yog qhov kev hloov pauv no?
A transformation T from a vector space V to a vector space W is called injective (los yog one-to-one) if T(u)=T(v) implies u=v. Hauv lwm lo lus, T yog txhaj tshuaj yog tias txhua tus vector hauv qhov chaw lub hom phiaj yog "ntaus" los ntawm feem ntau ib tus vector los ntawm qhov chaw sau npe.
Dab tsi yog daim ntawv qhia kev txhaj tshuaj linear?
A muaj nuj nqi f:X →Y f: X → Y los ntawm ib txheej X rau ib txheej Y yog hu ua ib-rau-ib (lossis txhaj tshuaj) yog thaum twg f(x)=f(x′) f (x)=f (x′) rau ib txhiax, x′∈X x, x′ ∈ X nws yuav tsum tuav tias x=x′. x=x ′. Qhov kev ua f yog hu mus rau (lossis qhov kev xav) yog tias rau tag nrho y∈Y y ∈ Y muaj muaj x∈X x ∈ X xws li f(x)=y.
